State assignment of finite-state machines

The state assignment problem of finite state machines (FSMs) is addressed. State assignment is a mapping from the set of states (symbolic names) of an FSM to the set of binary codes with the objective of minimising the area of the combinational circuit required to realise the FSM. It is one of the most important optimisation problems in the automatic synthesis of sequential circuits, since it has a major impact on the area, speed, power and testability of the circuits. The problem of finding an optimal state assignment is NP-hard. A new scheme is presented based on mean field annealing (MFA) to solve the graph embedding problem which is the main step in the state assignment process. The MFA algorithm combines the characteristics of simulated annealing and the Hopfield neural network. To solve the problem by MFA, the graph embedding problem is mapped into a neural network and an energy function is formulated. Experiments over the MCNC FSM benchmarks demonstrate that the proposed MFA algorithm can produce superior results, compared with the specialised methods such as the MUSTANG, NOVA and genetic algorithm